Design of Finite Time Reduced Order H∞ Controller for Linear Discrete Time Systems

Mohammed Taoussi (), Nabil El Akchioui, Adil Bardane, Nabil El Fezazi, Rashid Farkous, El Houssaine Tissir and Mo’tassem Al-Arydah ()
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Mohammed Taoussi: Industrial Technologies and Services Laboratory, Higher School of Technology, Sidi Mohammed Ben Abdellah University, Fez 30000, Morocco
Nabil El Akchioui: LRDSI Laboratory, Department of Physics, Faculty of Sciences and Technology, Abdelmalek Essaâdi University, Al Hoceima 32000, Morocco
Adil Bardane: Department of Physics, Khalifa University, Abu Dhabi P.O. Box 127788, United Arab Emirates
Nabil El Fezazi: LISAC Laboratory, Department of Physics, Faculty of Sciences Dhar El Mehraz, Sidi Mohammed Ben Abdellah University, Fez 30000, Morocco
Rashid Farkous: LISAC Laboratory, Department of Physics, Faculty of Sciences Dhar El Mehraz, Sidi Mohammed Ben Abdellah University, Fez 30000, Morocco
El Houssaine Tissir: LISAC Laboratory, Department of Physics, Faculty of Sciences Dhar El Mehraz, Sidi Mohammed Ben Abdellah University, Fez 30000, Morocco
Mo’tassem Al-Arydah: Department of Mathematics, Khalifa University, Abu Dhabi P.O. Box 127788, United Arab Emirates

Mathematics, 2022, vol. 11, issue 1, 1-17

Abstract: The current article gives a new approach that is efficient for the design of a low-order H∞ controller over a finite time interval. The system under consideration is a linear discrete time system affected by norm bounded disturbances. The proposed method has the advantage that takes into account both robustness aspects and desired closed-loop characteristics, reducing the number of variables in Linear Matrix Inequalities (LMIs). Thus, reduced order H∞ controller parameters are given to guarantee a finite time H∞ bound (FTB-H∞) for a closed-loop system. The method of the finite time stability, that is proven in this paper by the Lyapunov theory, can be applied to a wide range of process models. Numerical examples demonstrating the effectiveness of the results developed are presented at the end of this paper.

Keywords: finite time; discrete time system; disturbances; robustness; reduced order controller (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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